MATHEMATICS HIGH SCHOOL

Manny makes dinner using 1 box of pasta and 1 jar of sauce. If pasta is sold in packages of 10 boxes and sauce is sold in packages of 2 jars, what is the least number of dinners that Manny can make without any supplies leftover?

Answers

Answer 1

Answer:

10 dinners

Step-by-step explanation:

We solve using the Least Common Multiple Method.

We are told:

Pasta is sold in packages of 10 boxes Sauce is sold in packages of 2 jars.

We find the Multiples of 2 and 10

Multiples of 2:

2, 4, 6, 8, 10, 12, 14

Multiples of 10:

10, 20, 30

Therefore,

LCM(2, 10) = 10

The least number of dinners that Manny can make without any supplies leftover is 10 dinners

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In the pair of similar trapezoids, what is the length of side DA?

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$(|EH|)/(|GH|)=(|AD|)/(|CD|)\n\n(15)/(20)=(|AD|)/(60)\n(3)/(4)=(|AD|)/(60)\n4|AD|=180\n|AD|=45$

Assuming that there are 10 digits used as telephone number and the area code is a fixed 3 digit number. How many different telephone numbers could be created?

Answers

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A recipe for stew calls for 2 pounds of beef to serve 4 people. Gina wants to serve 8 people. How many pounds of beef should she use?

Answers

For serving 8 peoples, 4 pounds of beef is needed.

What is a linear function? What is a mathematical function, equation and expression?

function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.

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Given is that a recipe for stew calls for 2 pounds of beef to serve 4 people. Gina wants to serve 8 people.

It is given that it requires 2 pounds of beef to serve 4 people.

For 1 people, it will take (2/4) or 1/2 pounds of beef.

So, for serving 8 peoples, (1/2) x 8 or 4 pounds of beef is needed.

Therefore, for serving 8 peoples, 4 pounds of beef is needed.

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Gina will need 4 pounds of beef because 2×2=4.

83. Use properties of exponents to rewrite each expression with only positive, rational exponents. Then find the numerical value of each expression when x = 9, y= 8, and z= 16. In each case, the expression evaluates to a rational number.b. 11√y2z4

Answers

Answer:

$2^{(18)/(11)}$

Step-by-step explanation:

The given expression is

$\sqrt[11]{y^2z^4}$

The exponent property $\sqrt[n]{x^ay^b}=x^(a/n)y^(b/n)$

Applying this exponent property, we have

$\sqrt[11]{y^2z^4}\n\n=y^(2/11)z^(4/11)$

Now, the given numeric values are x = 9, y= 8, and z= 16

On substituting these values in the simplified expression, we get

$(2)^(2/11)(16)^(4/11)$

This can be further simplified by writing $16=2^4$

$(2)^(2/11)(2^4)^(4/11)\n\n(2)^(2/11)(2)^(16/11)$

Now, applying the product rule of exponent: $x^a\cdot x^b=x^(a+b)$

$(2)^(2/11+16/11)\n\n=2^{(18)/(11)}$

Use the elimination method to solve the system of equations.choose the correct ordered.4x+7y=60
-4x+7y=-4

Answers

A) 4x+7y=60
B) -4x+7y=-4
Adding the 2 equations
14y = 56
y = 4

A) 4x+7*4=60

A) 4x+28=60
A) 4x = 32
x = 8

Dixie packaging co has contracted to manufacture a box with no top that is to be made by removing squares of width x from the corners of a 15-in by 60-in piece of cardboard.a) Write a function for the VOLUME of the box as a function of x.

b) Determine x so that the volume of the box is at least 450 cubic inches.

c) Determine x so that the volume of the box is maximum.

Answers

The volume of the box as a function of x V(x) = x ( 60 -2x )( 15-2x )

The volume of the box as a function of x inches 0.55 inches ≤ x ≤ 6.79

The volume of the box is maximum x ≥ 6.79 inches

Given ,

The box with no top that is to be made by removing squares of width x

The corners of a 15-in by 60-in piece of cardboard.

Volume can be represented by this function below

V(x) = x ( 60 -2x )( 15-2x )

Where : x = height , ( 60 - 2x ) = length , ( 15 -2x ) = width

The volume of the box as a function of x is V(x) = x ( 60 -2x )( 15-2x )

To determine x so that,

The volume of the box ≥ 450 inches

V(x) = x ( 60 -2x )( 15-2x )

The volume of the box is at least 450 cubic inches.0.55 inches ≤ x ≤ 6.79 inches

The value of x for which volume of the box is maximum will be x ≥ 6.79 inches.

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//httpsbrainly.com/question/23245822

Answer:

a) V(x) = x ( 60 -2x )( 15-2x )

b) 0.55 inches ≤ x ≤ 6.79 inches

c) x ≥ 6.79 inches

Step-by-step explanation:

Given data:

No top, cardboard dimensions ; 15-in by 60-in

a) A function for the volume of the box as a function of x the Volume can be represented by this function below

= V(x) = x ( 60 -2x )( 15-2x )

where : x = height , ( 60 - 2x ) = length , ( 15 -2x ) = width

b) determine x so that the volume of the box ≥ 450 inches

450 = x( 60 - 2x ) ( 15 -2x ) ( solving the equation )

0.55 inches ≤ x ≤ 6.79 inches

c ) The value of x for which volume of the box is maximum

will be x ≥ 6.79 inches

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